The viscous behavior of polymers in nanometer scale volumes can significantly differ from bulk, due to the large free surfaces and the dominating molecular heterogeneity at nanoscale. In this study, we present the first experimental investigation on the creep and strain rate behavior of electrospun polyacrylonitrile (PAN) nanofibers. The apparatus used in this study was a MEMS-based platform, developed by the authors with the addition of a feedback loop to (a) maintain constant force on a nanofiber during a creep experiment and (b) vary the applied strain rate to investigate the viscoplastic response of amorphous polymer nanofibers. The creep compliance was found to be highly dependent on the nanofiber diameter, increasing with its diameter. In agreement with previous literature studies, it was concluded that the higher stiffness of thinner nanofibers was due to higher molecular alignment. A semi-empirical model was proposed to describe the experimentally determined viscous response of the PAN nanofibers, was composed of a Langevin spring and an Eyring's dashpot to capture the strain rate sensitive yield stress and the orientation hardening observed in our experiments. The present experiments coupled with the semi-empirical model are among the first efforts to understand viscous phenomena at the nanoscale.